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  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/08%3A_Combinatorics/8.03%3A_Permutations
    An r -permutation of A is an ordered selection of r distinct elements from A . In other words, it is the linear arrangement of r distinct objects.  It appears in many other forms and names. T...An r -permutation of A is an ordered selection of r distinct elements from A . In other words, it is the linear arrangement of r distinct objects.  It appears in many other forms and names. The number of permutations of n objects, taken r at a time without replacement. The number of ways to arrange n objects (in a sequence), taken r at a time without replacement.
  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_(Morris)/02%3A_Enumeration/03%3A_Permutations_Combinations_and_the_Binomial_Theorem/3.01%3A_Permutations
    We begin by looking at permutations, because these are a straightforward application of the product rule. The word “permutation” means a rearrangement, and this is exactly what a permutation is: an or...We begin by looking at permutations, because these are a straightforward application of the product rule. The word “permutation” means a rearrangement, and this is exactly what a permutation is: an ordering of a number of distinct items in a line. Sometimes even though we have a large number of distinct items, we want to single out a smaller number and arrange those into a line; this is also a sort of permutation.
  • https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/7%3A_Combinatorics/7.3%3A_Permutations
    Let A be the set of all linear r-permutations of the n objects, and let B be the set of all circular r-permutations. Given any r-permutation, form its image by joining its “hea...Let A be the set of all linear r-permutations of the n objects, and let B be the set of all circular r-permutations. Given any r-permutation, form its image by joining its “head” to its ”tail.” It becomes clear, using the same argument in the proof above, that f is an r-to-one function, which means f maps r distinct elements from A to the same image in B.

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